Simplify the following expression: $ z = \dfrac{p - 10}{7} - \dfrac{-5}{8} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{p - 10}{7} \times \dfrac{8}{8} = \dfrac{8p - 80}{56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-5}{8} \times \dfrac{7}{7} = \dfrac{-35}{56} $ Therefore $ z = \dfrac{8p - 80}{56} - \dfrac{-35}{56} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{8p - 80 + 35 }{56} $ Distribute the negative sign: $z = \dfrac{8p - 80 + 35}{56}$ $z = \dfrac{8p - 45}{56}$